Modelling porous structures by repeated Sierpinski carpets

Porous materials such as sedimentary rocks often show a fractal character a t certain length scales. Deterministic fractal generators, iterated upto se veral stages and then repeated periodically, provide a realistic model for such systems. On the fractal, diffusion is anomalous, and obeys the law (r( 2)) similar to t(2/dw), where (r(2)) is the mean square distance covered in time t and d(w) >2 is the random walk dimension. The question is: How is t he macroscopic diffusivity related to the characteristics of the small scal e fractal structure, which is hidden in the large-scale homogeneous materia l? In particular, do structures with same d(w) necessarily lead to the same diffusion coefficient at the same iteration stage? The present paper tries to shed some light on these questions. (C) 2001 Elsevier Science B.V. All rights reserved.